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diffalg[greater] - compare the rank of two differential polynomials

Calling Sequence

greater (p, q, R)

Parameters

p, q

-

differential polynomials in R

R

-

differential polynomial ring

Description

• 

Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

• 

The function greater returns true if the rank of p is greater than the one of q. Otherwise, false is returned.

• 

p has greater rank than q if

  

(a)  q belongs to the ground field of R and p does not,

  

(b)  the leader of p is greater than the leader of q with respect to the ranking of R, or

  

(c)  p and q have the same leader  and the degree,  in  this common leader,  of  p is greater than the one of  q.

• 

The function greater provides only a pre-order on R.

• 

The command with(diffalg,greater) allows the use of the abbreviated form of this command.

Examples

Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

withdiffalg:

R:=differential_ringderivations=x,y,ranking=lexu

R:=PDE_ring

(1)

greaterux,uy,y,R

true

(2)

greaterux,x2+uy,uy,y5ux,x2+1,R

false

(3)

See Also

diffalg(deprecated), diffalg(deprecated)/differential_algebra, diffalg(deprecated)/differential_ring, diffalg(deprecated)[derivatives], diffalg(deprecated)[leader], DifferentialAlgebra[Get], DifferentialAlgebra[Is]


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